How Tide Prediction Works: From the Moon to Your Local Tide Chart
If you've ever checked a tide chart before heading out to fish, surf, or launch a boat, you've relied on one of the most accurate forecasts in all of science. Weather forecasters struggle to predict rain five days out, but tide predictions for a given harbor can be made years in advance and still land within a few inches and a few minutes of what actually happens. That's not luck — it's because tides, unlike weather, are driven by something almost perfectly predictable: the mechanics of the solar system.
Here's an overview of how tide prediction actually works, from the forces that generate tides to the math that turns a month of water-level data into a tide table you can check on your Tydebox or phone.
What Actually Causes a Tide
Tides are generated by the gravitational pull of the moon and sun on the Earth's oceans. The moon does most of the work — even though the sun is about 27 million times more massive than the moon, it's also 93 million miles away, and tidal force falls off with the cube of distance. That distance penalty means the moon's tidal pull is roughly twice as strong as the sun's, despite the sun's enormous mass advantage.
The simplest way to picture it: the Earth and moon orbit a common center of mass. On the side of the Earth facing the moon, the moon's gravity slightly overpowers the centrifugal effect of that orbit, pulling water into a bulge. On the far side of the Earth, the opposite happens — centrifugal force wins out, creating a second bulge facing away from the moon. As the Earth rotates underneath these two bulges roughly once a day, most coastlines experience two high tides and two low tides every 24 hours and 50 minutes (a "lunar day," slightly longer than a solar day because the moon is also moving in its orbit).
That's the astronomy. But astronomy alone doesn't tell you how big your local tide will be — for that, you need hydrodynamics.
Why Your Bay's Tide Isn't the Same as the Open Ocean's
The tide-generating forces from the moon and sun are actually tiny — far too small on their own to create the dramatic tides seen in places like the Bay of Fundy (over 50 feet of range) or Cook Inlet, Alaska. What they do generate is a very long, very low wave moving across the open ocean, sometimes only a foot high. When that wave reaches a continental shelf, then a coastline, then narrows into a bay or estuary, it gets amplified — sometimes dramatically — depending on the length, width, and depth of that waterway.
This is why two towns 50 miles apart on the same coast can have wildly different tide ranges and timing. It's also why shallow water distorts the shape of the tide curve, generates secondary "overtide" frequencies, and interacts with river flow and storm surge in ways that pure astronomy can't predict. Accurate tide prediction has to account for both pieces: the astronomical forcing that determines when tidal energy shows up, and the local hydrodynamics that determine how big it gets and how it behaves once it gets there.
The Building Blocks: Tidal Constituents
Here's the key insight that makes tide prediction possible at all: the tide isn't one wave — it's the sum of dozens of individual waves, called tidal constituents, each with its own fixed frequency tied to a specific astronomical cycle. Because the orbits and rotations that drive the tide are extremely stable and well understood, we know exactly what those frequencies are, even before collecting a single day of data.
A few of the biggest players:
M2 — the main lunar semidiurnal constituent, with a period of 12.42 hours. This is usually the largest constituent almost everywhere, and it's the one most responsible for the basic "two highs, two lows a day" pattern.
S2 — the main solar semidiurnal constituent, period exactly 12.00 hours. When M2 and S2 line up (around new and full moon), their effects add together, producing the larger spring tides. When they're out of phase (around the first and third quarter moon), they partially cancel, producing smaller neap tides.
N2 — captures the effect of the moon's elliptical orbit (the tide is stronger at lunar perigee, weaker at apogee).
K1 and O1 — diurnal constituents that capture the effect of the moon (and sun) being north or south of the equator. Where K1 and O1 are large relative to M2, you get a diurnal tide (one high and one low per day) instead of a semidiurnal one.
Every location on Earth has its own unique fingerprint of amplitudes and phase lags for these constituents, shaped by local hydrodynamics. That fingerprint — usually 30-plus constituents for a typical harbor — is what actually gets used to make a prediction.
Turning Water-Level Data Into a Forecast: Harmonic Analysis
So how do you find the fingerprint for a specific harbor? You measure water level continuously for a period of time — ideally a full year, though useful results can come from as little as a month — and then run a harmonic analysis on the data.
The intuition behind harmonic analysis is easier than it sounds. Imagine chopping your water-level record into consecutive segments, each exactly 12.42 hours long (the M2 period), and stacking them on top of each other. The M2 contribution lines up perfectly in every segment and reinforces itself, while every other constituent — since its period doesn't match 12.42 hours — drifts out of alignment from segment to segment and gradually cancels out when averaged. What's left is a clean picture of the M2 wave: its height (amplitude) and its timing relative to the moon (phase lag, called the epoch). Repeat that process using each constituent's own specific period, and you can extract every wave in the mix.
In practice, modern harmonic analysis uses least-squares fitting rather than this literal stacking method, but the underlying logic is the same. And it explains a practical rule of thumb: separating two constituents with very close frequencies (like the main lunar and solar tides, or the two main diurnal tides) requires a correspondingly long data record — weeks for some pairs, a full six months or more for others. This minimum record length is called the synodic period, and it's why one month of data gives a decent tide prediction, but a full year gives a meaningfully better one.
The Actual Prediction: Summing Cosine Waves
Once you have the amplitude and phase lag for every constituent at a station, generating a prediction is just addition. The height of the tide at any time t is computed as:
h(t) = H₀ + Σ fᵢ Hᵢ cos(aᵢt + [V₀+u]ᵢ − κᵢ)
In plain terms: start with the average water level (H₀), then add up a cosine wave for every constituent (M2, S2, N2, K1, O1, and dozens more), each with its own amplitude (H), its own known frequency (a), and its own phase lag (κ) measured from the harmonic analysis. A small correction factor (f) adjusts each constituent's amplitude for the 18.6-year cycle in the moon's orbital plane, which slowly modulates tide ranges over almost two decades.
Run that equation forward in time — for a day, a month, or 20 years — and you get a full predicted tide curve. Software then scans that curve to pick out the specific times and heights of each high and low water, which is what shows up on a typical tide chart.
From One Harbor to Thousands of Locations
Running a full harmonic analysis requires a long, high-quality water-level record, and that's only practical at a limited number of reference stations — major, well-instrumented harbors that have recorded data for years. But mariners need predictions for thousands of smaller subordinate stations — coves, inlets, and secondary ports that never had their own tide gauge.
The solution: compare short-term water-level observations at a subordinate station to the predicted highs and lows at the nearest reference station with similar tidal behavior, then compute a simple time offset and height ratio between the two. Apply that fixed offset to the reference station's daily prediction, and you get a serviceable forecast for the subordinate station — which is exactly how the "Table 2" differences in a traditional tide table are built. Modern digital tide products, like the kind you'd see in a tide app, use the same underlying science: harmonic constituents at reference stations, computed forward with the prediction equation, and adjusted for nearby locations.
A Few Important Caveats
Tide predictions are astronomical forecasts, not weather forecasts. They tell you what the tide would do under average atmospheric conditions. Real-world water levels can run higher or lower than predicted because of:
Storm surge — wind and low atmospheric pressure piling water up or pulling it away from shore
River flow — heavy runoff can suppress the tide range and shift timing, especially in estuaries
Long-term sea level change — land subsidence, glacial rebound, or gradual sea level rise can shift the baseline over years or decades
That's why harbors get their reference datums (like Mean Lower Low Water, the standard for U.S. nautical charts) recalculated periodically, and why a tide app's prediction can differ from what you actually see at the dock during a storm.
The Takeaway
Tide prediction is a remarkable example of how a well-understood physical system — the orbits of the Earth, moon, and sun — combines with local geography to produce forecasts that are both deeply mathematical and remarkably reliable. Every tide chart you've ever checked is really a sum of a few dozen cosine waves, each tied to a specific astronomical rhythm, tuned to your specific stretch of coastline by measuring the water itself.
This post draws on Tidal Analysis and Prediction (NOAA Special Publication NOS CO-OPS 3) by Bruce B. Parker, Center for Operational Oceanographic Products and Services, National Ocean Service, NOAA, 2007.